Let X₁, X₂,..., X, be a random sample of size 9 from a normal distribution N (54,10) and Y,,Y,,Y, Y, be a random sample of size 4 from an independent normal distribution N (54,12). Compute P 0.546 Σ(x-x) Σ(X-Y)² i=l <61.09
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- Suppose that three random variables X1, X2, X3 form a random sample from the uniform distribution on interval [0, 1]. Determine the value of E[(X1-2X2+X3)2]Suppose that X1, . . . , Xn form a random sample from the uniform distribution on the interval [θ1, θ2], where both θ1 and θ2 are unknown (−∞ < θ1 < θ2 < ∞). Find the MOM estimates of θ1 and θ2.Suppose that the random variables X1,...,Xn form a random sample of size n from the uniform distribution on the interval [0, 1]. Let Y1 = min{X1,. . .,Xn}, and let Yn = max{X1,...,Xn}. Find E(Y1) and E(Yn).
- Let X1 and X2 be observations of a random sample of size n = 2 from a Cauchy Distribution.Find P(X1 < −1 and 1 < X2)Let X1, …, Xn be a random sample from a population with the Poisson(λ) distribution. Find the MLE of λ.Let X1, X2, ... , Xn be a random sample, normally distributed with mean μ and variance σ2If σ2 is unknown, find a minimum value for n to guarantee, with probability 0.90, that a 0.95 CI for μ will have length no more than σ/4 explain.
- Let x and y be random variable such that the mean and variance of X are 2 and 4. respectively, while the mean and variance of y are 6 and k, respectively. A sample of size 4 is taken from the x-distribution and a sample of size 9 is taken from the y-distribution .If p[(x-y)>8]=0.0228,then what is the value of the constant k?Let X1 , X2 ,....., X25 be a random sample drawn from a population with mean of 75 and standard deviation of 25.Then µx is A. 25B. 75C. 15D. 5Suppose that X has a discrete uniform distribution on the integers 0 through 9. Determine the mean, variance, and standard deviation of the random variable Y = 5X and compare to the corresponding results for X.
- Suppose x has a distribution with μ = 15 and σ = 12. (a) If a random sample of size n = 35 is drawn, find μx, σ x and P(15 ≤ x ≤ 17). (Round σx to two decimal places and the probability to four decimal places.) μx = σ x = P(15 ≤ x ≤ 17) = (b) If a random sample of size n = 59 is drawn, find μx, σ x and P(15 ≤ x ≤ 17). (Round σ x to two decimal places and the probability to four decimal places.) μx = σ x = P(15 ≤ x ≤ 17) =Suppose x has a distribution with μ = 60 and σ = 17. (a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means? No, the sample size is too small. Yes, the x distribution is normal with mean μ x = 60 and σ x = 4.25. Yes, the x distribution is normal with mean μ x = 60 and σ x = 17 Yes, the x distribution is normal with mean μ x = 60 and σ x = 1.1. (b) If the original x distribution is normal, can we say anything about the x distribution of random samples of size 16? No, the sample size is too small. Yes, the x distribution is normal with mean μ x = 60 and σ x = 17. Yes, the x distribution is normal with mean μ x = 60 and σ x = 1.1. Yes, the x distribution is normal with mean μ x = 60 and σ x = 4.25. (c) Find P(56 ≤ x ≤ 61). (Round your answer to four decimal places.)Suppose x has a distribution with μ = 60 and σ = 17. (a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means? No, the sample size is too small. Yes, the x distribution is normal with mean μ x = 60 and σ x = 4.25. Yes, the x distribution is normal with mean μ x = 60 and σ x = 17 Yes, the x distribution is normal with mean μ x = 60 and σ x = 1.1. (b) If the original x distribution is normal, can we say anything about the x distribution of random samples of size 16? No, the sample size is too small. Yes, the x distribution is normal with mean μ x = 60 and σ x = 17. Yes, the x distribution is normal with mean μ x = 60 and σ x = 1.1. Yes, the x distribution is normal with mean μ x = 60 and σ x = 4.25. Find P(56 ≤ x ≤ 61). (Round your answer to four decimal places.)